Imaging lens and imaging apparatus equipped with the imaging lens

ABSTRACT

An imaging lens is substantially constituted by five lenses, including: a positive first lens having a convex surface toward the object side; a negative second lens having a concave surface toward the object side; a positive third lens of a meniscus shape with a convex surface toward the object side; a positive fourth lens of a meniscus shape with a concave surface toward the object side; and a negative fifth lens having a concave surface toward the image side, the surface thereof toward the image side being of an aspherical shape having at least one inflection point within a range from an intersection of a principal light ray at a maximum angle of view with the surface toward the image side inwardly toward the optical axis in the radial direction, provided in this order from the object side. The imaging lens satisfies predetermined conditional formulae.

CROSS REFERENCE TO RELATED APPLICATIONS

The present application claims priority under 35 U.S.C. §119 to JapanesePatent Application No. 2014-003430 filed on Jan. 10, 2014. The aboveapplication is hereby expressly incorporated by reference, in itsentirety, into the present application.

BACKGROUND OF THE INVENTION

1. Technical Field

The present invention is related to a fixed focus imaging lens forforming optical images of subjects onto an imaging element such as a CCD(Charge Coupled Device) and a CMOS (Complementary Metal OxideSemiconductor). The present invention is also related to an imagingapparatus provided with the imaging lens that performs photography suchas a digital still camera, a cellular telephone with a built in camera,a PDA (Personal Digital Assistant), a smart phone, a tablet typeterminal, and a portable gaming device.

2. Background Art

Accompanying the recent spread of personal computers in households,digital still cameras capable of inputting image data such asphotographed scenes and portraits into personal computers are rapidlybecoming available. In addition, many cellular telephones, smart phones,and tablet type terminals are being equipped with camera modules forinputting images. Imaging elements such as CCD's and CMOS's are employedin these devices having photography functions. Recently, miniaturizationof these imaging elements is advancing, and there is demand forminiaturization of the entirety of the photography devices as well asimaging lenses to be mounted thereon. At the same time, the number ofpixels in imaging elements is increasing, and there is demand for highresolution and high performance of imaging lenses. Performancecorresponding to 5 megapixels or greater, and more preferably 8megapixels or greater, is desired.

In response to such demands, imaging lenses having a five lensconfiguration, which is a comparatively large number of lenses, havebeen proposed. For example, Chinese Utility Model Publication No.202815300, Taiwanese Patent Publication No. 201305652 and U.S. Pat. No.8,179,614 propose imaging lenses with five lens configurations,constituted by: a first lens having a positive refractive power, asecond lens having a negative refractive power, a third lens having apositive refractive power, a fourth lens having a positive refractivepower, and a fifth lens having a negative refractive power, provided inthis order from the object side.

DISCLOSURE OF THE INVENTION

Meanwhile, the image sizes of imaging elements are increasingaccompanying the demand for a greater number of pixels, with respect toimaging lenses for use in apparatuses which are becoming thinner such assmart phones and tablet terminals. There is increased demand for thetotal lengths of lenses to be shortened further with respect to theimage sizes of imaging elements having large image sizes that satisfythe demand for a greater number of pixels. In connection with the demandfor increased resolution, there is demand for imaging lenses havingsmaller F numbers to be realized. However, the imaging lenses disclosedin Chinese Utility Model Publication No. 202815300, Taiwanese PatentPublication No. 201305652 and U.S. Pat. No. 8,179,614 are not favorably,because the total lengths of these lenses will become excessively longif applied to imaging elements that satisfy the demand for a greaternumber of pixels. Further, smaller F numbers are desired for the imaginglenses disclosed in Chinese Utility Model Publication No. 202815300,Taiwanese Patent Publication No. 201305652 and U.S. Pat. No. 8,179,614.

The present invention has been developed in view of the foregoingpoints. The object of the present invention is to provide an imaginglens that can realize a shortening of the total length with respect toimage sizes so as to be compatible with large imaging elements having agreater numbers of pixels, a small F number, and high imagingperformance from a central angle of view to peripheral angles of view.It is another object of the present invention to provide an imagingapparatus equipped with the lens, which is capable of obtaining highresolution photographed images.

An imaging lens of the present invention substantially consists of fivelenses, including:

a first lens having a positive refractive power and a convex surfacetoward the object side;

a second lens having a negative refractive power and a concave surfacetoward the object side;

a third lens having a positive refractive power and is of a meniscusshape with a convex surface toward the object side;

a fourth lens having a positive refractive power and is of a meniscusshape with a concave surface toward the object side; and

a fifth lens having a negative refractive power and a concave surfacetoward the image side, the surface thereof toward the image side beingof an aspherical shape having at least one inflection point within arange from an intersection of a principal light ray at a maximum angleof view with the surface toward the image side inwardly toward theoptical axis in the radial direction, provided in this order from theobject side;

the imaging lens satisfying the following conditional formulae:

1.25<f/f1<3  (1)

0.57<f/f4<3  (2)

−1.87<f/f5<−0.5  (3)

1<TTL/(f·tan ω)<1.56  (4)

wherein f is the focal length of the entire system, f1 is the focallength of the first lens, f4 is the focal length of the fourth lens, f5is the focal length of the fifth lens, TTL is the distance from thesurface of the first lens toward the object side to the imaging surfacealong the optical axis in the case that back focus is an air convertedlength, and ω is the half value of a maximum angle of view when focusedon an object at infinity.

The optical performance of the imaging lens of the present invention canbe further improved by adopting the following favorable configurations.

In the imaging lens of the present invention, it is preferable for thesurface of the second lens toward the object side to be of an asphericalshape having at least one inflection point within a range from anintersection of a marginal axial light ray with the surface toward theobject side inwardly toward the optical axis in the radial direction.

In the imaging lens of the present invention, it is preferable for thesurface of the third lens toward the object side to be of an asphericalshape having at least one inflection point within a range from anintersection of a marginal axial light ray with the surface toward theobject side inwardly toward the optical axis in the radial direction.

It is preferable for the imaging lens of the present invention tofurther comprise an aperture stop positioned at the object side of thesurface of the first lens toward the object side.

It is preferable for the imaging lens of the present invention tosatisfy one or arbitrary combinations of Conditional Formulae (5), (6),(1-1) through (5-1), (1-2) through (5-2), (1-3), (3-3), and (4-3) below.

1.32<f/f1<2.32  (1-1)

1.32<f/f1<2  (1-2)

1.35<f/f1<1.86  (1-3)

0.73<f/f4<2.19  (2-1)

0.8<f/f4<1.79  (2-2)

−1.71<f/f5<−0.77  (3-1)

−1.71<f/f5<−0.92  (3-2)

−1.64<f/f5<−0.92  (3-3)

1.25<TTL/(f·tan ω)<1.49  (4-1)

1.34<TTL/(f·tan ω)<1.49  (4-2)

1.34<TTL/(f·tan ω)<1.47  (4-3)

0.6<L1f/Φ<0.88  (5)

0.7<L1f/Φ<0.85  (5-1)

0.75<L1f/Φ<0.82  (5-2)

1<f·tan ω/L5r<3  (6)

wherein f is the focal length of the entire system, f1 is the focallength of the first lens, f4 is the focal length of the fourth lens, f5is the focal length of the fifth lens, TTL is the distance from thesurface of the first lens toward the object side to the imaging surfacealong the optical axis in the case that back focus is an air convertedlength, f is the focal length of the entire system, ω is the half valueof a maximum angle of view when focused on an object at infinity, L1 fis the paraxial radius of curvature of the surface of the first lenstoward the object side, Φ is the diameter of the entrance pupil, and L5r is the paraxial radius of curvature of the surface of the fifth lenstoward the image side.

Note that in the imaging lens of the present invention, the expression“substantially consists of five lenses” means that the imaging lens ofthe present invention may also include lenses that practically have nopower, optical elements other than lenses such as a stop and a coverglass, and mechanical components such as lens flanges, a lens barrel, acamera shake correcting mechanism, etc., in addition to the five lenses.

Note also that the shapes of the surfaces of the lenses and the signs ofthe refractive indices thereof are considered in the paraxial region inthe case that the lenses include aspherical surfaces. The signs of therefractive indices are positive for surfaces having convex surfacestoward the object side, and negative for surfaces having convex surfacestoward the image side.

In addition, the “inflection point” refers to a point at which the shapeof a surface changes from a convex shape to a concave shape (or from aconcave shape to a convex shape) with respect to the image side.

An imaging apparatus of the present invention is equipped with theimaging lens of the present invention.

According to the imaging lens of the present invention, theconfiguration of each lens element is optimized within a lensconfiguration having five lenses as a whole, and the shapes of the firstlens through the fifth lens are favorably configured in particular.Therefore, a lens system that can achieve a short total length withrespect to image sizes which is compatible with an imaging element of asize that satisfies demand for a greater number of pixels, whileachieving a small F number, and realizes high imaging performance from acentral angle of view to peripheral angles of view can be realized.

The imaging apparatus of the present invention is equipped with theimaging lens of the present invention. Therefore, the apparatus size canbe shortened in the direction of the optical axis of the imaging lens,and the imaging apparatus of the present invention is capable ofobtaining high resolution photographed images.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a sectional diagram that illustrates a first example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 1.

FIG. 2 is a sectional diagram that illustrates a second example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 2.

FIG. 3 is a sectional diagram that illustrates a third example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 3.

FIG. 4 is a sectional diagram that illustrates a fourth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 4.

FIG. 5 is a sectional diagram that illustrates a fifth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 5.

FIG. 6 is a sectional diagram that illustrates a sixth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 6.

FIG. 7 is a sectional diagram that illustrates a sixth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 7.

FIG. 8 is a sectional diagram that illustrates a sixth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 8.

FIG. 9 is a sectional diagram that illustrates a sixth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 9.

FIG. 10 is a sectional diagram that illustrates a sixth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 10.

FIG. 11 is a sectional diagram that illustrates a sixth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 11.

FIG. 12 is a sectional diagram that illustrates a sixth example of theconfiguration of an imaging lens according to an embodiment of thepresent invention, and corresponds to a lens of Example 12.

FIG. 13 is a diagram that illustrates the paths of light rays that passthrough the imaging lens of FIG. 1.

FIG. 14 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 1, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 15 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 2, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 16 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 3, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 17 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 4, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 18 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 5, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 19 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 6, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 20 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 7, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 21 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 8, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 22 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 9, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 23 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 10, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 24 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 11, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 25 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 12, wherein the diagrams illustrate sphericalaberration, astigmatism, distortion, and lateral chromatic aberration,in this order from the left side of the drawing sheet.

FIG. 26 is a diagram that illustrates a cellular telephone as an imagingapparatus equipped with the imaging lens of the present invention.

FIG. 27 is a diagram that illustrates a smart phone as an imagingapparatus equipped with the imaging lens of the present invention.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, embodiments of the present invention will be described indetail with reference to the attached drawings.

FIG. 1 illustrates a first example of the configuration of an imaginglens according to an embodiment of the present invention. This examplecorresponds to the lens configuration of Numerical Example 1 (Table 1and Table 2), to be described later. Similarly, FIG. 2 through FIG. 12are sectional diagrams that illustrate second through twelfths examplesof lens configurations that correspond to Numerical Examples 2 through12 (Table 3 through Table 24). In FIGS. 1 through 12, the symbol Rirepresents the radii of curvature of ith surfaces, i being lens surfacenumbers that sequentially increase from the object side to the imageside, with the surface of a lens element most toward the object sidedesignated as first. The symbol Di represents the distances between anith surface and an i+1st surface along an optical axis Z1. Note that thebasic configurations of the examples are the same, and therefore adescription will be given of the imaging lens of FIG. 1 as a base, andthe examples of FIGS. 2 through 12 will also be described as necessary.In addition, FIG. 13 is a diagram that illustrates the paths of lightrays that pass through the imaging lens of FIG. 1. FIG. 13 illustratesthe paths of an axial light beam 2 and a maximum angle of view lightbeam 3 in a state focused on an object at a distance of infinity, aswell as a half value ω of a maximum angle of view. Note that withrespect to the maximum angle of view light beam 3, a principal light ray4 at the maximum angle of view is indicated by a dashed and dotted line.

The imaging lens L of the embodiment of the present invention isfavorably employed in various imaging devices that employ imagingelements such as a CCD and a CMOS. The imaging lens L of the embodimentof the present invention is particularly favorable for use incomparatively miniature portable terminal devices, such as a digitalstill camera, a cellular telephone with a built in camera, a smartphone, a tablet type terminal, and a PDA. The imaging lens L is equippedwith a first lens L1, a second lens L2, a third lens L3, a fourth lensL4, and a fifth lens L5, provided in this order from the object side.

FIG. 26 schematically illustrates a cellular telephone as an imagingapparatus 1 according to an embodiment of the present invention. Theimaging apparatus 1 of the embodiment of the present invention isequipped with the imaging lens L according to the embodiment of thepresent invention and an imaging element 100 (refer to FIGS. 1 through12) such as a CCD that outputs image signals corresponding to opticalimages formed by the imaging lens L. The imaging element 100 is providedat an image formation plane of the imaging lens L.

FIG. 27 schematically illustrates a smart phone as an imaging apparatus501 according to an embodiment of the present invention. The imagingapparatus 501 of the embodiment of the present invention is equippedwith a camera section 541 having the imaging lens L according to theembodiment of the present invention and an imaging element 100 (refer toFIGS. 1 through 12) such as a CCD that outputs image signalscorresponding to optical images formed by the imaging lens L. Theimaging element 100 is provided at an image formation plane of theimaging lens L.

Various optical members CG may be provided between the fifth lens L5 andthe imaging element 100, depending on the configuration of the camera towhich the lens is applied. A planar optical member such as a cover glassfor protecting an imaging surface and an infrared cutoff filter may beprovided, for example. In this case, a planar cover glass having acoating having a filtering effect such as an infrared cutoff filtercoating or an ND filter coating, or a material that exhibits similareffects, may be utilized as the optical member CG.

Alternatively, the optical member CG may be omitted, and a coating maybe administered on the fifth lens L5 to obtain the same effect as thatof the optical member CG. In this case, the number of parts can bereduced, and the total length can be shortened.

It is preferable for the imaging lens L to be equipped with an aperturestop St positioned at the object side of the surface of the first lensL1 toward the object side. In the case that the aperture stop Stpositioned in this manner, increases in the incident angles of lightrays that pass through the optical system and enter the image formationplane (imaging element) can be suppressed, particularly at theperipheral portions of an imaging region. Note that the expression“positioned at the object side of the surface of the first lens L1toward the object side” means that the position of the aperture stop inthe direction of the optical axis is at the same position as theintersection of marginal axial rays of light and the surface of thefirst lens L1 toward the object side, or more toward the object sidethan this position.

Further, in the case that the aperture stop St is positioned at theobject side of the surface of the first lens L1 toward the object sidein the direction of the optical axis, it is preferable for the aperturestop St to be positioned at the image side of the apex of the surface ofthe first lens L1 toward the object side. In the case that the aperturestop St is positioned at the image side of the apex of the surface ofthe first lens L1 toward the object side in this manner, the totallength of the imaging lens including the aperture stop St can beshortened. Note that the imaging lenses L of Examples 1 through 12 areexamples of configurations in which the aperture stop St is positionedat the object side of the surface of the first lens L1 toward the objectside, and positioned at the image side of the apex of the surface of thefirst lens L1 toward the object side. Alternatively, the aperture stopSt may be positioned at the object side of the apex of the surface ofthe first lens L1 toward the object side. A case in which the aperturestop St is positioned at the object side of the apex of the surface ofthe first lens L1 toward the object side is somewhat disadvantageousfrom the viewpoint of securing peripheral light compared to a case inwhich the aperture stop St is positioned at the image side of the apexof the surface of the first lens L1 toward the object side. However,increases in the incident angles of light rays at peripheral portions ofan imaging region that enter the image formation plane (imaging element)can be more favorably suppressed. Note that the aperture stops Stillustrated in FIG. 1 through FIG. 12 do not necessarily represent thesizes or shapes thereof, but indicate the positions thereof on theoptical axis Z1.

In the imaging lens L, the first lens L1 has a positive refractive powerin the vicinity of the optical axis. This configuration is advantageousfrom the viewpoint of shortening the total length of the lens. Inaddition, the first lens L1 has a convex surface toward the object sidein the vicinity of the optical axis. Thereby, the positive refractivepower of the first lens L1, which performs a substantial portion of theimage forming function, can be sufficiently increased. As a result,shortening of the total length of the lens can be more favorablyrealized. In addition, it is preferable for the first lens L1 to be of abiconvex shape in the vicinity of the optical axis. In this case, thesecond lens L2, which has a concave surface toward the object side inthe vicinity of the optical axis, can be provided adjacent to the firstlens L1, which is of a biconvex shape in the vicinity of the opticalaxis, at the image side thereof, and spherical aberration can befavorably corrected. In addition, the first lens L1 may be of a meniscusshape having a convex surface toward the object side in the vicinity ofthe optical axis. In this case, the rearward principal point of thefirst lens L1 can be moved toward the object side, and a shortening ofthe total length can be more favorably realized.

The second lens L2 has a negative refractive power in the vicinity ofthe optical axis. The second lens L2 has a concave surface toward theobject side in the vicinity of the optical axis. Thereby, sphericalaberration and chromatic aberration can be favorably corrected. Inaddition, the second lens L2 may be of a meniscus shape having a concavesurface toward the object side in the vicinity of the optical axis. Inthis case, spherical aberration and chromatic aberration can be morefavorably corrected. Alternatively, the second lens L2 may be of abiconcave shape in the vicinity of the optical axis. In this case, thegeneration of higher order spherical aberration can be favorablysuppressed.

In addition, it is preferable for the surface of the second lens L2toward the object side to be of an aspherical shape having at least oneinflection point within a range from an intersection of a marginal axiallight ray with the surface toward the object side inwardly toward theoptical axis in the radial direction. In this case, the surface of thesecond lens L2 toward the object side can be configured to be convextoward the object side at the peripheral portions thereof, and thegeneration of higher order spherical aberration can be favorablysuppressed. Note that in the present specification, the expression“within a range from an intersection of a marginal axial light ray withthe surface toward the object side inwardly toward the optical axis inthe radial direction” refers to a position at the intersection of thesurface toward the object side and the axial marginal light ray andpositions along the radial direction toward the optical axis therefrom.The inflection point may be provided on the surface of the second lensL2 toward the object side at any arbitrary position from among theposition at the intersection of the surface toward the object side andthe axial marginal light ray and positions along the radial directiontoward the optical axis therefrom.

The third lens L3 has a positive refractive power in the vicinity of theoptical axis. Thereby, correction of spherical aberration and chromaticaberration is facilitated. In addition, the third lens L3 is of ameniscus shape having a convex surface toward the object side in thevicinity of the optical axis. Thereby, the rearward principal point ofthe third lens L3 can be moved toward the object side, and the totallength of the lens can be favorably shortened.

In addition, it is preferable for the surface of the third lens L3toward the object side to be of an aspherical shape having at least oneinflection point within a range from an intersection of a marginal axiallight ray with the surface toward the object side inwardly toward theoptical axis in the radial direction. In this case, the surface of thethird lens L3 toward the object side can be configured to be concavetoward the object side at the peripheral portions thereof, and thegeneration of astigmatism at large angles of view can be favorablysuppressed. The inflection point may be provided on the surface of thethird lens L3 toward the object side at any arbitrary position fromamong the position at the intersection of the surface toward the objectside and the axial marginal light ray and positions along the radialdirection toward the optical axis therefrom.

The fourth lens L4 has a positive refractive power in the vicinity ofthe optical axis. In this case, increases in the incident angles oflight rays that pass through the optical system and enter the imageformation plane (imaging element) can be suppressed, particularly atintermediate angles of view. In addition, the fourth lens L4 is of ameniscus shape having a concave surface toward the object side in thevicinity of the optical axis. Thereby, astigmatism can be favorablycorrected.

The fifth lens L5 has a negative refractive power in the vicinity of theoptical axis. Thereby, shortening of the total length of the lens can befavorably realized, and field curvature can be favorably corrected. Inaddition, the fifth lens L5 has a concave surface toward the image sidein the vicinity of the optical axis. This configuration is even moreadvantageous from the viewpoint of correcting field curvature. It ispreferable for the fifth lens L5 to be of a meniscus shape having aconvex surface toward the object side in the vicinity of the opticalaxis, in order to cause this advantageous effect to become moreprominent. Alternatively, the fifth lens L5 may be of a biconcave shapein the vicinity of the optical axis. In this case, it becomes easy toimpart the fifth lens L5, which his the lens provided most toward theimage side in the imaging lens L, with a sufficiently strong negativerefractive power, and a shortening of the total length can be morefavorably realized.

In addition, the surface of the fifth lens L5 toward the image side isof an aspherical shape having at least one inflection point within arange from an intersection of a principal light ray at a maximum angleof view with the surface toward the image side inwardly toward theoptical axis in the radial direction. Thereby, increases in the incidentangles of light rays that pass through the optical system and enter theimage formation plane (imaging element) can be suppressed, particularlyat the peripheral portions of the imaging region. In addition,distortion can be favorably corrected by the surface of the fifth lensL5 toward the image side being of an aspherical shape having at leastone inflection point within a range from the intersection of a principallight ray at a maximum angle of view with the surface toward the imageside inwardly toward the optical axis in the radial direction. Note thatin the present specification, the expression “within a range from anintersection of a principal light ray at a maximum angle of view withthe surface toward the image side inwardly toward the optical axis inthe radial direction” refers to a position at the intersection of thesurface toward the image side and the principal light ray at the maximumangle of view and positions along the radial direction toward theoptical axis therefrom. The inflection point may be provided on thesurface of the fifth lens L5 toward the image side at any arbitraryposition from among the position at the intersection of the surfacetoward the image side and the principal light ray at the maximum angleof view and positions along the radial direction toward the optical axistherefrom.

According to the imaging lens L described above, the configurations ofeach of the first lens L1 through the fifth lens L5 are optimized aslens elements in a lens configuration having a total of five lenses.Therefore, a lens system having a shortened total length with respect toimage sizes which is compatible with an imaging element of a size thatsatisfies demand for a greater number of pixels, that also achieves asmall F number, and realizes high imaging performance from a centralangle of view to peripheral angles of view, can be realized.

It is preferable for at least one of the surfaces of each of the firstlens L1 through the fifth lens L5 of the imaging lens L to be anaspherical surface, in order to improve performance.

In addition, it is preferable for each of the first lens L1 through thefifth lens L5 that constitute the imaging lens L to be a single lens,not a cemented lens. If all of the lenses are single lenses, the numberof lens surfaces in contact with air will be greater than a case inwhich some of the lenses are cemented lenses. Therefore, the degree offreedom in the design of each lens will increase. As a result,shortening of the total length and increase in resolution will befacilitated. As a result, shortening of the total length of the lenswith respect to image sizes and the realization of a smaller F number isfacilitated to a greater degree.

Next, the operation and effects of conditional formulae related to theimaging lens L configured as described above will be described ingreater detail. Note that it is preferable for the imaging lens L tosatisfy any one of the following conditional formulae, or arbitrarycombinations of the following conditional formulae. It is preferable forthe conditional formulae to be satisfied to be selected as appropriateaccording to the items required of the imaging lens L.

First, it is preferable for the focal length f1 of the first lens L1 andthe focal length f of the entire system to satisfy Conditional Formula(1) below.

1.25<f/f1<3  (1)

Conditional Formula (1) defines a preferable range of numerical valuesfor the ratio of the focal length f of the entire system with respect tothe focal length f1 of the first lens L1. By securing the refractivepower of the first lens L1 such that the value of f/f1 is not less thanor equal to the lower limit defined in Conditional Formula (1), thepositive refractive power of the first lens L1 will not becomeexcessively weak with respect to the refractive power of the entiresystem. As a result, a shortening of the total length of the lens can befavorably realized. In addition, satisfying the lower limit ofConditional Formula (1) is advantageous from the viewpoint of decreasingthe ratio of the focal length f of the entire system with respect to thetotal length of the lens. By suppressing the refractive power of thefirst lens L1 such that the value of f/f1 is not greater than or equalto the upper limit defined in Conditional Formula (1), the positiverefractive power of the first lens L1 will not become excessively strongwith respect to the refractive power of the entire system. As a result,spherical aberration and astigmatism can be favorably corrected. Inaddition, because spherical aberration can be favorably corrected bysatisfying the upper limit of Conditional Formula (1), thisconfiguration is advantageous from the viewpoint of achieving an evensmaller F number. It is preferable for Conditional Formula (1-1) to besatisfied, more preferable for Conditional Formula (1-2) to besatisfied, and even more preferable for Conditional Formula (1-3) to besatisfied, in order to cause these advantageous effects to become moreprominent.

1.32<f/f1<2.32  (1-1)

1.32<f/f1<2  (1-2)

1.35<f/f1<1.86  (1-3)

In addition, it is preferable for the focal length f4 of the fourth lensL4 and the focal length f of the entire system to satisfy ConditionalFormula (2) below.

0.57<f/f4<3  (2)

Conditional Formula (2) defines a preferable range of numerical valuesfor the ratio of the focal length f of the entire system with respect tothe focal length f4 of the fourth lens L4. By securing the refractivepower of the fourth lens L4 such that the value of f/f4 is not less thanor equal to the lower limit defined in Conditional Formula (2), thepositive refractive power of the fourth lens L4 will not becomeexcessively weak with respect to the refractive power of the entiresystem. This configuration is advantageous from the viewpoint ofrealizing a shortening of the total length of the lens. In addition, bysecuring the refractive power of the fourth lens L4 such that the valueof f/f4 is not less than or equal to the lower limit defined inConditional Formula (2), a portion of the positive refractive power ofthe imaging lens L as a whole can be appropriately borne by the fourthlens L4. As a result, spherical aberration can be corrected, and thisconfiguration is also advantageous from the viewpoint of decreasing theF number. By suppressing the refractive power of the fourth lens L4 suchthat the value of f/f4 is not greater than or equal to the upper limitdefined in Conditional Formula (2), the positive refractive power of thefourth lens L4 will not become excessively strong with respect to therefractive power of the entire system. As a result, field curvature canbe favorably corrected. It is preferable for Conditional Formula (2-1)to be satisfied, and more preferable for Conditional Formula (2-2) to besatisfied, in order to cause these advantageous effects to become moreprominent.

0.73<f/f4<2.19  (2-1)

0.8<f/f4<1.79  (2-2)

It is preferable for the focal length f5 of the fifth lens L5 and thefocal length f of the entire system to satisfy Conditional Formula (3)below.

−1.87<f/f5<−0.5  (3)

Conditional Formula (3) defines a preferable range of numerical valuesfor the ratio of the focal length f of the entire system with respect tothe focal length f5 of the fifth lens L5. By suppressing the refractivepower of the fifth lens L5 such that the value of f/f5 is not less thanor equal to the lower limit defined in Conditional Formula (3), thenegative refractive power of the fifth lens L5 will not becomeexcessively strong with respect to the refractive power of the entiresystem. As a result, increases in the incident angles of light rays thatpass through the optical system and enter the image formation plane(imaging element) can be suppressed at intermediate angles of view. Inaddition, there is a tendency for back focus to become shortaccompanying a shortening of the total length of the lens. However, theamount of back focus can be maintained, by satisfying the lower limit ofConditional Formula (3). By securing the refractive power of the fifthlens L5 such that the value of f/f5 is not greater than or equal to theupper limit defined in Conditional Formula (3), the negative refractivepower of the fifth lens L5 will not become excessively weak with respectto the refractive power of the entire system. As a result, fieldcurvature can be favorably corrected. In addition, if the first lens L1through the fourth lens L4 are considered to constitute a first lensgroup having a positive refractive power and the fifth lens L5 isconsidered to constitute a second lens group having a negativerefractive power, the imaging lens L has a telephoto type configurationas a whole. There is a tendency for the length of the first lens groupalong the optical axis to increase when attempting to decrease the Fnumber in imaging lenses having such a telephoto type configuration,resulting in an increase in the total length of the lens. By satisfyingthe upper limit of Conditional Formula (3), the negative refractivepower of the fifth lens L5 can be secured, and therefore suppressing theincrease in the length of the first lens group along the optical axisthat accompanies the realization of a small F number is facilitated. Itis preferable for Conditional Formula (3-1) to be satisfied, morepreferable for Conditional Formula (3-2) to be satisfied, and even morepreferable for Conditional Formula (3-3) to be satisfied, in order tocause these advantageous effects to become more prominent.

−1.71<f/f5<−0.77  (3-1)

−1.71<f/f5<−0.92  (3-2)

−1.64<f/f5<−0.92  (3-3)

In addition, it is preferable for the distance TTL from the surface ofthe first lens L1 toward the object side to the imaging surface alongthe optical axis in the case that back focus is an air converted lengthand a the paraxial image height (Ram) to satisfy Conditional Formula (4)below.

1<TTL/(f·tan ω)<1.56  (4)

Conditional Formula (4) defines a preferable range of numerical valuesfor the ratio of the distance TTL from the surface of the first lens L1toward the object side to the imaging surface along the optical axis(total length of the lens) with respect to the paraxial image height (ftan Note that the back focus (the distance from the apex of the surfaceof the fifth lens L5 toward the image side to the imaging surface) is anair converted length in the total length of the lens. By securing thedistance TTL from the surface of the first lens L1 toward the objectside to the imaging surface with respect to the paraxial image height(f·tan ω) such that the value of TTL/(f·tan ω) is not less than or equalto the lower limit defined in Conditional Formula (4), astigmatism canbe favorably corrected, and increases in the incident angles of lightrays that pass through the optical system and enter the image formationplane (imaging element) can be suppressed. By maintaining the distanceTTL from the surface of the first lens L1 toward the object side to theimaging surface with respect to the paraxial image height (f·tan ω) suchthat the value of TTL/(f·tan ω) is not greater than or equal to theupper limit defined in Conditional Formula (4), the total length of thelens with respect to image sizes can be favorably shortened. For thisreason, satisfying Conditional Formula (4) is advantageous from theviewpoint of configuring the imaging lens to be compatible with imagingelements that satisfy demand for a greater number of pixels, and fromthe viewpoint of maintaining an image size while further shortening thetotal length of the lens. It is preferable for Conditional Formula (4-1)to be satisfied, more preferable for Conditional Formula (4-2) to besatisfied, and even more preferable for Conditional Formula (4-3) to besatisfied, in order to cause these advantageous effects to become moreprominent.

1.25<TTL/(f·tan ω)<1.49  (4-1)

1.34<TTL/(f·tan ω)<1.49  (4-2)

1.34<TTL/(f·tan ω)<1.47  (4-3)

In addition, it is preferable for the paraxial radius of curvature L1 fof the surface of the first lens L1 toward the object side and thediameter Φ of the entrance pupil to satisfy Conditional Formula (5)below.

0.6<L1f/Φ<0.88  (5)

Conditional Formula (5) defines a preferable range of numerical valuesfor the paraxial radius of curvature L1 f of the surface of the firstlens L1 toward the object side with respect to the diameter Φ of theentrance pupil. By setting the paraxial radius of curvature L1 f of thesurface of the first lens L1 toward the object side with respect to thediameter Φ of the entrance pupil such that the value of L1 f/Φ is notless than or equal to the lower limit defined in Conditional Formula(5), the absolute value of the paraxial radius of curvature L1 f of thesurface of the first lens L1 toward the object side will not becomeexcessively small with respect to the diameter Φ of the entrance pupil,and the generation of spherical aberration can be suppressed. By settingthe paraxial radius of curvature L1 f of the surface of the first lensL1 toward the object side with respect to the diameter Φ of the entrancepupil such that the value of L1 f/Φ is not greater than or equal to theupper limit defined in Conditional Formula (5), the absolute value ofthe paraxial radius of curvature L1 f of the surface of the first lensL1 toward the object side will not become excessively great with respectto the diameter Φ of the entrance pupil. This configuration isadvantageous from the viewpoint of shortening the total length of thelens while realizing a small F number. It is preferable for ConditionalFormula (5-1) to be satisfied, and even more preferable for ConditionalFormula (5-2) to be satisfied in order to cause these advantageouseffects to become more prominent.

0.7<L1f/Φ<0.85  (5-1)

0.75<L1f/Φ<0.82  (5-2)

In addition, it is preferable for the focal length f of the entiresystem, the half value ω of the maximum angle of view in a state focusedon an object at infinity, and the paraxial radius of curvature L5 r ofthe surface of the fifth lens L5 toward the image side to satisfyConditional Formula (6) below.

1<f·tan ω/L5r<3  (6)

Conditional Formula (6) defines a preferable range of numerical valuesfor the ratio of the paraxial image height (f·tan ω) with respect to theparaxial radius of curvature L5 r of the surface of the fifth lens L5toward the image side. By setting the image height (f·tan ω) withrespect to the paraxial radius of curvature of the surface of the fifthlens L5 toward the image side such that the value of f·tan ω/L5 r is notless than or equal to the lower limit defined in Conditional Formula(6), the absolute value of the paraxial radius of curvature L5 r of thesurface of the fifth lens L5 toward the image side, which is the surfacemost toward the image side in the imaging lens, will not becomeexcessively great. As a result, a shortening of the total length of thelens can be realized, while field curvature can be sufficientlycorrected. Note that if the fifth lens L5 has a concave surface towardthe image side and is of an aspherical shape having at least oneinflection point as shown in the imaging lenses L of each of theExamples and the lower limit of Conditional Formula (6) is satisfied,field curvature can be favorably corrected from a central angle of viewto peripheral angles of view. This configuration is favorable from theviewpoint of realizing a wider angle of view. By setting the imageheight (f·tan ω) with respect to the paraxial radius of curvature of thesurface of the fifth lens L5 toward the image side such that the valueof f·tan ω/L5 r is not greater than or equal to the upper limit definedin Conditional Formula (6), the absolute value of the paraxial radius ofcurvature L5 r of the surface of the fifth lens L5 toward the imageside, which is the surface most toward the image side in the imaginglens, will not become excessively small. This will result in increasesin the incident angles of light rays that pass through the opticalsystem and enter the image formation plane (imaging element) beingsuppressed, particularly at intermediate angles of view. In addition,excessive correction of field curvature can be suppressed.

Further improved imaging performance can be realized in the imaginglenses according to the embodiments of the present invention bysatisfying the above preferred conditions appropriately. In addition,the imaging apparatuses according to the embodiments of the presentinvention output image signals corresponding to optical images formed bythe high performance imaging lenses according to the embodiments of thepresent invention. Therefore, photographed images having high resolutioncan be obtained, while achieving a shortening of the apparatus size.

In addition, in the case that the lens configurations of each of thefirst lens L1 through the fifth lens L5 are set such that the maximumangle of view in a state focused on an object at infinity is 75 degreesor greater as in the imaging lenses of the first through twelfthembodiments, a shortening of the total length of the lens with respectto image sizes can be realized, and the imaging lens L may be favorablyapplied for use with imaging elements that satisfy demand regardingincreased resolution, such as those in cellular telephones. Further, inthe case that the lens configurations of each of the first lens L1through the fifth lens L5 are set such that the value of ConditionalFormula (4), which defines the ratio of the total length of the lenswith respect to the paraxial image height, is within a range from 1.39to 1.46 as in the imaging lenses of the first through twelfthembodiments, a shortening of the total length of the lens with respectto image sizes can be favorably achieved, and the imaging lens L can bemore favorably applied to cellular telephones and the like tat satisfydemand for an increased number of pixels. In contrast, the imaginglenses disclosed in Chinese Utility Model Publication No. 202815300,Taiwanese Patent Publication No. 201305652, and U.S. Pat. No. 8,179,614have narrow maximum angles of view of 72.4 degrees to 73.6 degrees, andthe values thereof corresponding to Conditional Formula (4) are 1.59 to1.69, which are large values. Therefore, the total lengths of theselenses are excessively long with respect to image sizes, and it isdifficult for these lenses to be applied to imaging elements thatsatisfy demand for an increased number of pixels.

In addition, in the case that the lens configurations of each of thefirst lens L1 through the fifth lens L5 of the imaging lens L are setsuch that the F number is less than 2.1 as in the imaging lenses of thefirst through twelfth embodiments, demand for higher resolution can befavorably satisfied. In contrast, the imaging lenses disclosed inChinese Utility Model Publication No. 202815300, Taiwanese PatentPublication No. 201305652 and U.S. Pat. No. 8,179,614 have F numbers ofapproximately 2.2 to 2.6, which are large values, and it is difficultfor these lenses to sufficiently satisfy demand for higher resolution.

Next, specific examples of numerical values of the imaging lens of thepresent invention will be described. A plurality of examples ofnumerical values will be summarized and explained below.

Table 1 and Table 2 below show specific lens data corresponding to theconfiguration of the imaging lens illustrated in FIG. 1. Table 1 showsbasic lens data of the imaging lens, and Table 2 shows data related toaspherical surfaces. In the lens data of Table 1, ith lens surfacenumbers that sequentially increase from the object side to the imageside, with surface of an optical element most toward the object sidedesignated as first, are shown in the column Si for the imaging lens ofExample 1. The radii of curvature (mm) of ith surfaces from the objectside corresponding to the symbols Ri illustrated in FIG. 1 are shown inthe column Ri. Similarly, the distances (mm) between an ith surface Siand an i+1st surface Si+1 from the object side along the optical axis Zare shown in the column Di. The refractive indices of jth opticalelements from the object side with respect to the d line (wavelength:587.6 nm) are shown in the column Ndj. The Abbe's numbers of the jthoptical elements with respect to the d line are shown in the column vdj.

Table 1 also shows the aperture stop St and the optical member CG. Thesigns of the radii of curvature are positive for surface shapes havingconvex surfaces toward the object side, and negative for surface shapeshaving convex surfaces toward the image side. In addition, the values ofthe focal length f (mm) of the entire system, the back focus Bf (mm),the F number Fno., and the maximum angle of view 2ω (°) are shown asdata above the lens data. Note that the back focus Bf is represented asan air converted value.

A “*” mark is appended to the surface numbers of aspherical surfaces inthe basic lens data of Table 1. In the imaging lens of Example 1, bothof the surfaces of the first lens L1 through the fifth lens L5 are allaspherical in shape. In the basic lens data of Table 1, numerical valuesof radii of curvature in the vicinity of the optical axis (paraxialradii of curvature) are shown as the radii of curvature of theaspherical surfaces.

Table 2 shows aspherical surface data of the imaging lens of Example 1.In the numerical values shown as the aspherical surface data, the symbol“E” indicates that the numerical value following thereafter is a “powerindex” having 10 as a base, and that the numerical value represented bythe index function having 10 as a base is to be multiplied by thenumerical value in front of “E”. For example, “1.0E-02” indicates thatthe numerical value is “1.0·10⁻²”.

The values of coefficients An and KA represented by the asphericalsurface shape formula (A) below are shown as the aspherical surfacedata. In greater detail, Z is the length (mm) of a normal line thatextends from a point on the aspherical surface having a height h to aplane (a plane perpendicular to the optical axis) that contacts the apexof the aspherical surface.

$\begin{matrix}{Z = {\frac{C \times h^{2}}{1 + \sqrt{1 - {{KA} \times C^{2} \times h^{2}}}} + {\sum\limits_{n}^{\;}{{An} \times h^{n}}}}} & (A)\end{matrix}$

wherein: Z is the depth of the aspherical surface (mm), h is thedistance from the optical axis to the surface of the lens (height) (mm),C is the paraxial curvature=1/R (R is the paraxial radius of curvature),An is an nth ordinal aspherical surface coefficient (n is an integer 3or greater), and KA is an aspherical surface coefficient.

Specific lens data corresponding to the configurations of the imaginglenses illustrated in FIG. 2 through FIG. 12 are shown in Table 3through Table 24 as Example 2 through Example 12. In the imaging lensesof Examples 1 through 12, both of the surfaces of the first lens L1through the fifth lens L5 are all aspherical surfaces.

FIG. 14 is a collection of diagrams that illustrate aberrations of theimaging lens of Example 1, wherein the diagrams illustrate the sphericalaberration, the astigmatism, the distortion and the lateral chromaticaberration (chromatic aberration of magnification) of the imaging lensof Example 1, respectively, in this order from the left side of thedrawing sheet. Each of the diagrams that illustrate the sphericalaberration, the astigmatism (field curvature), and the distortionillustrate aberrations using the d line (wavelength: 587.6 nm) as areference wavelength. The diagram that illustrates spherical aberrationalso shows aberrations related to the F line (wavelength: 486.1 nm), theC line (wavelength: 656.3 nm), and the g line (wavelength: 435.8 nm).The diagram that illustrates lateral chromatic aberration showsaberrations related to the F line, the C line, and the g line. In thediagram that illustrates astigmatism, aberration in the sagittaldirection (S) is indicated by a solid line, while aberration in thetangential direction (T) is indicated by a broken line. In addition,“Fno.” denotes F numbers, and “ω” denotes a half value of the maximumangle of view in a state focused on an object at infinity.

Similarly, the aberrations of the imaging lens of Example 2 throughExample 12 are illustrated in FIG. 15 through FIG. 25. The diagrams thatillustrate aberrations in FIG. 15 through FIG. 25 are for those in whichthe object distance is infinity.

Table 25 shows values corresponding to Conditional Formulae (1) through(6), respectively summarized for each of Examples 1 through 12.

Note that each of the tables show numerical values which are rounded offat a predetermined number of digits. With respect to the units of thenumerical values, “°” is used for degrees and “mm” is used for lengths.However, these are merely examples, and other appropriate units may beemployed, because it is possible to utilize optical systems if they areproportionately enlarged or proportionately miniaturized.

As can be understood from each set of numerical value data and from thediagrams that illustrate aberrations, the imaging lenses of Examples 1through 12 have widened maximum angles of view of 75° or greater in astate focused on an object at infinity, shortened total lengths withrespect to image sizes, small F numbers, favorably correct variousaberrations, and realize high imaging performance from a central angleof view to peripheral angles of view.

The present invention has been described using the embodiments and theExamples. However, the imaging lens of the present invention is notlimited to the embodiments and Examples described above, and variousmodifications are possible. For example, the values of the radii ofcurvature, the distances among surfaces, the refractive indices, theAbbe's numbers, the aspherical surface coefficients, etc., are notlimited to the numerical values indicated in connection with theExamples of numerical values, and may be other values.

In addition, the Examples are described under the presumption that theyare to be utilized with fixed focus. However, it is also possible forconfigurations capable of adjusting focus to be adopted. It is possibleto adopt a configuration, in which the entirety of the lens system isfed out or a portion of the lenses is moved along the optical axis toenable automatic focus, for example.

TABLE 1 Examlpe 1 f = 3.767, Bf = 1.094, Fno = 2.00, 2ω = 76.4 Si Ri DiNdj νdj 1 (aperture stop) ∞ −0.262 *2 1.43576 0.634 1.54488 54.87 *3−12.56934 0.092 *4 −2.35699 0.263 1.63350 23.62 *5 −16.07808 0.249 *65.63909 0.264 1.63350 23.62 *7 7.63431 0.367 *8 −1.95808 0.546 1.5448854.87 *9 −1.14178 0.458 *10  7.75851 0.354 1.54488 54.87 *11  1.387450.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.547 14 (imaging surface) ∞*aspherical surface

TABLE 2 Example 1: Aspherical Surface Data Surface Number KA A3 A4 A5 A62 1.5168655E−01 0.0000000E+00 −1.0454134E−01 −2.6958694E−01  7.2587716E+00 3 1.0000036E+01 0.0000000E+00 −7.2644420E−011.2758826E+01 −8.6664213E+01 4 −3.2768625E+00  0.0000000E+00 4.9022628E−01 8.2614684E−01 −4.0624899E+00 5 7.7034942E+000.0000000E+00  4.6789121E−01 2.9825689E−01 −3.2333113E+00 63.2308970E+00 0.0000000E+00 −7.7254782E−03 1.0063226E−01 −2.2506005E−017 −1.0000010E+01  0.0000000E+00  5.0041563E−02 5.6109469E−05−7.2677891E−01 8 1.3383687E+00 0.0000000E+00 −7.1727695E−019.4585234E+00 −5.8147083E+01 9 −2.2746098E−01  0.0000000E+00−2.2305772E−01 5.0516532E+00 −3.2023084E+01 10 6.5610332E+000.0000000E+00 −4.2822713E−01 7.9293467E−02  4.1716014E−01 11−3.7654842E−01  0.0000000E+00 −6.4688393E−01 6.3746941E−02 2.1514692E+00 A7 A8 A9 A10 A11 2 −2.8048064E+01  3.3826067E+01 3.9043285E+01 −1.3942081E+02   6.1642095E+01 3 3.0477755E+02−4.6608991E+02  −3.0826969E+02 2.3836100E+03 −3.2749909E+03 4−1.9765907E+00  2.8167359E+01 −3.6761845E+01 −2.3187133E+01  8.1642056E+01 5 6.1099143E+00 −3.6440001E+00  −4.4608697E+006.0853642E+00  6.8606483E+00 6 −4.7276044E+00  2.1493248E+01−4.0225648E+01 2.8184446E+01  8.0057402E+00 7 1.8236128E+00−2.1199288E+00  −5.3998949E−01 4.0293236E+00 −3.9970522E+00 82.0966361E+02 −4.5360653E+02   5.4934823E+02 −2.1867000E+02 −3.4964734E+02 9 1.0331759E+02 −1.8987932E+02   1.8956656E+02−5.2522543E+01  −1.0380268E+02 10 −3.6893183E−02  −3.5262732E−01  7.3058144E−02 1.1591844E−01 −1.4846381E−02 11 −4.7105049E+00 5.9567842E+00 −5.2702655E+00 3.4922808E+00 −1.8850932E+00 A12 A13 A14A15 A16 2 2.0645114E+02 −3.5642456E+02   2.4498692E+02 −7.7875941E+01  8.9233794E+00 3 −1.1287596E+02  5.3135126E+03 −6.4714377E+033.4058663E+03 −6.9948882E+02 4 −5.6736613E+01  5.7746806E+01−1.3107300E+02 1.2452639E+02 −3.9402224E+01 5 −1.5133811E+01 4.3973260E+00  6.9587903E+00 −6.1082130E+00   1.6181071E+00 6−2.0078308E+01  3.3260149E+01 −7.9379791E+01 8.3198900E+01−2.9919267E+01 7 1.1727333E+00 −2.4710029E−01   2.6686835E+00−3.4001513E+00   1.2209693E+00 8 6.1184295E+02 −4.2873837E+02  1.5460863E+02 −2.7244814E+01   1.8844510E+00 9 1.3668683E+02−6.9790346E+01   1.2362950E+01 2.1299920E+00 −8.3025679E−01 10−2.6262138E−02  1.9001913E−03  3.5016404E−03 −4.3132952E−04 −7.9646632E−05 11 8.9978563E−01 −3.6692393E−01   1.0952244E−01−1.9734302E−02   1.5650554E−03

TABLE 3 Example 2 f = 3.660, Bf = 1.109, Fno. = 2.02, 2ω = 79.4 Si Ri DiNdj νdj 1 (aperture stop) ∞ −0.221 *2 1.48711 0.576 1.54488 54.87 *3−48.69923 0.090 *4 −2.59267 0.258 1.63350 23.62 *5 −11.74413 0.144 *62.69604 0.256 1.63350 23.62 *7 2.63066 0.483 *8 −3.37527 0.710 1.5448854.87 *9 −1.07355 0.414 *10  65.78190 0.261 1.54488 54.87 *11  1.232840.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.562 14 (imaging surface) ∞*aspherical surface

TABLE 4 Example 2: Aspherical Surface Data Surface Number KA A3 A4 A5 A62 −1.4088685E+00 0.0000000E+00  6.8322612E−02 −5.3240416E−01  4.6053536E+00 3 −7.7480709E+00 0.0000000E+00 −3.4870417E−013.0571700E+00 −1.5166393E+01 4 −2.8757546E+01 0.0000000E+00−8.1078728E−02 1.5975657E+00 −7.6273157E+00 5 −1.9425292E+000.0000000E+00 −7.8675452E−02 3.4850945E+00 −2.0997923E+01 6−3.9293239E+00 0.0000000E+00 −5.0613466E−01 2.3139225E+00 −8.3239934E+007 −1.9602572E−01 0.0000000E+00 −3.2821284E−02 −4.8828018E−01  7.9968368E−01 8 −3.8745971E−01 0.0000000E+00 −8.8598471E−021.1310818E+00 −2.0860026E+00 9  3.2506603E−01 0.0000000E+00 6.4224152E−01 −4.4916262E+00   2.1136598E+01 10  1.5510672E+000.0000000E+00 −2.6976787E−01 1.2241351E−01 −1.3578743E−01 11−1.7430779E−01 0.0000000E+00 −7.4487498E−01 8.2529406E−01 −3.8404107E−01A7 A8 A9 A10 A11 2 −1.5351350E+01 2.2267411E+01 −9.8051395E+005.9443522E+00 −5.6621313E+01 3  4.5362648E+01 −7.4108755E+01 −1.5795975E+00 2.8861210E+02 −6.0063409E+02 4  2.2891870E+01−4.7993237E+01   6.2211437E+01 −6.6383894E+00  −1.3020378E+02 5 7.5979423E+01 −1.7161782E+02   2.1243348E+02 −6.4125109E+01 −2.6839518E+01 6  2.4503298E+01 −8.8831607E+01   2.4721086E+02−3.2514548E+02  −3.1054662E+01 7 −2.1841829E−02 −9.0057662E−01 −1.6879037E+00 4.1178680E+00  5.2849658E+00 8 −1.7284114E+019.6099662E+01 −2.0106409E+02 1.8351386E+02 −1.9439067E+01 9−5.6744098E+01 8.4703239E+01 −5.6909364E+01 −1.5406461E+01  5.1768567E+01 10  6.2516346E−01 −8.7472325E−01   5.4250310E−01−1.6031006E−01   1.3232722E−02 11  6.5700470E−02 8.5778834E−02−2.0286287E−01 1.7823424E−01 −5.0739758E−02 A12 A13 A14 A15 A16 2 1.1230858E+02 −8.6384485E+01   1.7341765E+01 1.0198367E+01−4.0841693E+00 3  4.8953907E+02 5.2288012E+01 −4.1149106E+022.9629176E+02 −7.1936083E+01 4  1.8272082E+02 −6.9135400E+00 −1.9502241E+02 1.7481367E+02 −4.9613923E+01 5 −6.3854470E+021.9894397E+03 −2.5542230E+03 1.5965718E+03 −4.0174613E+02 6 5.1332574E+02 −2.0141515E+02  −6.3904776E+02 7.6292601E+02−2.5665569E+02 7 −1.8834899E+01 1.4384166E+01  1.7302255E+00−6.7262874E+00   2.2783547E+00 8 −6.1938964E+01 −3.9601069E+01  1.2230152E+02 −7.8517137E+01   1.6944873E+01 9 −2.1176786E+01−1.8042773E+01   2.2251784E+01 −8.9474275E+00   1.3226049E+00 10 6.0436664E−03 1.4854825E−02 −2.2818661E−02 1.0572152E−02 −1.6382448E−0311 −2.0445611E−02 1.8662435E−02 −4.8058229E−03 3.5744103E−04 2.0389794E−05

TABLE 5 Example 3 f = 3.788, Bf = 1.069, Fno. = 2.03, 2ω = 77.6 Si Ri DiNdj νdj 1 (aperture stop) ∞ −0.262 *2 1.42644 0.629 1.54488 54.87 *3−13.39031 0.092 *4 −2.31126 0.263 1.63350 23.62 *5 −18.42257 0.262 *65.01172 0.263 1.63350 23.62 *7 6.75755 0.379 *8 −1.91735 0.524 1.5448854.87 *9 −1.05752 0.485 *10  −17.52208 0.354 1.54488 54.87 *11  1.680150.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.523 14 (imaging surface) ∞*aspherical surface

TABLE 6 Example 3: Aspherical Surface Data Surface Number KA A3 A4 A5 A62  1.5617651E−01 0.0000000E+00 3.5908002E−03 −1.2282705E+001.3758237E+01 3 −1.0000027E+01 0.0000000E+00 −1.5223800E−02  6.7090125E−01 −5.8295509E+00  4 −6.0860395E+00 0.0000000E+003.9070561E−01  3.7633582E−01 −2.6199103E+00  5 −9.8903529E+000.0000000E+00 3.7733058E−01  2.2547475E−01 −3.4239243E+00  6−9.0165841E+00 0.0000000E+00 −9.1430657E−02   6.0225993E−01−1.6886928E+00  7  6.2697268E+00 0.0000000E+00 2.1278097E−02−8.6342503E−01 7.1524197E+00 8  1.5584231E+00 0.0000000E+00−4.1114686E−01   3.4270636E+00 −1.2785486E+01  9 −9.6497860E−010.0000000E+00 3.7005516E−01 −3.2499672E+00 1.3750503E+01 10−9.9995984E+00 0.0000000E+00 −3.1230356E−01   1.1497589E−014.5344098E−01 11 −9.5381172E−02 0.0000000E+00 −5.6962115E−01  4.3220062E−01 2.6493152E−01 A7 A8 A9 A10 A11 2 −6.3119757E+011.6141218E+02 −2.5251914E+02   2.5671602E+02 −2.0042216E+02  3 3.7381553E+01 −1.1477674E+02  1.0188592E+02  2.9087589E+02−8.9105168E+02  4  5.1399314E−01 2.0740945E+00 4.9639170E+01−1.9002249E+02 2.6636112E+02 5  9.5959568E+00 −1.3584713E+01 1.0180291E+01 −8.6768206E+00 1.7993081E+01 6 −3.5995133E+007.9762377E+00 5.0059375E+01 −1.8489591E+02 1.8618758E+02 7−2.7489090E+01 4.3369429E+01 5.7718217E+00 −1.0813369E+02 8.1474874E+018  2.5373958E+01 −1.1590131E+01  −5.2292451E+01   9.0966532E+013.8214242E+00 9 −3.3020877E+01 4.3103908E+01 −1.9454516E+01 −1.9808382E+01 2.4148492E+01 10 −5.2109998E−01 1.1379419E−011.3261205E−01 −1.9563589E−01 1.6485447E−01 11 −6.0313682E−013.3030407E−01 4.2747465E−03 −8.9471649E−02 4.3463971E−02 A12 A13 A14 A15A16 2  1.7459731E+02 −1.7066791E+02  1.2407066E+02 −5.2124074E+019.5170032E+00 3  8.4271231E+02 4.8951974E+01 −7.0113308E+02  5.1408432E+02 −1.2378254E+02  4 −1.2366607E+02 −5.1843701E+01 4.5008218E+01  1.8969106E+01 −1.5019480E+01  5 −1.8615638E+01−3.9565066E−01  1.3285363E+01 −8.2460746E+00 1.4651464E+00 6 7.1439537E+01 −2.3035414E+02  5.4559251E+01  1.0398674E+02−5.4545428E+01  7  1.7369006E+02 −4.1195894E+02  3.7195233E+02−1.6490567E+02 2.9826495E+01 8 −1.4835979E+02 1.5602801E+02−5.4099151E+01  −5.2598559E+00 5.2340550E+00 9  7.9766494E+00−2.8899577E+01  2.1247916E+01 −7.0857981E+00 9.3860770E−01 10−3.8250387E−02 −4.4095944E−02  3.5585345E−02 −9.9966331E−031.0172441E−03 11 −7.4316464E−03 4.5890404E−05 −3.6611409E−04  2.6897452E−04 −4.3128688E−05 

TABLE 7 Example 4 f = 3.750, Bf = 1.187, Fno. = 2.02, 2ω = 78.0 Si Ri DiNdj νdj 1 (aperture stop) ∞ −0.262 *2 1.43885 0.635 1.54488 54.87 *3−13.81865 0.100 *4 −2.29167 0.263 1.63350 23.62 *5 −21.82640 0.240 *64.85071 0.263 1.63350 23.62 *7 6.46919 0.354 *8 −1.96456 0.511 1.5448854.87 *9 −1.03042 0.446 *10  −26.11317 0.327 1.54488 54.87 *11  1.727380.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.640 14 (imaging surface) ∞*aspherical surface

TABLE 8 Example 4: Aspherical Surface Data Surface Number KA A3 A4 A5 A62 1.3714018E−01 0.0000000E+00 −5.4234818E−02  −1.1819791E−01  2.6241389E+00 3 −7.0076611E+00  0.0000000E+00 −3.1977046E−01 6.2075180E+00 −4.7552452E+01 4 −6.1243782E+00  0.0000000E+004.7969938E−01 8.4351606E−02  4.3908215E−01 5 1.0000048E+01 0.0000000E+004.7327909E−01 6.0950527E−03 −1.9826252E+00 6 −9.8442398E+00 0.0000000E+00 −4.7892243E−02  −1.6164317E−01   6.9405485E+00 79.9235922E+00 0.0000000E+00 9.1654143E−02 5.2246119E−03 −2.7778854E+00 81.3243120E+00 0.0000000E+00 −7.7067437E−01  1.2192175E+01 −7.9203457E+019 −6.7170753E−01  0.0000000E+00 1.5693595E−01 −6.0103921E−01  2.6618617E−01 10 −1.0719747E+00  0.0000000E+00 −3.5562368E−01 2.0267353E−01  1.8414479E−01 11 −8.6143262E−02  0.0000000E+00−6.0725587E−01  5.5763959E−01 −1.0206528E−01 A7 A8 A9 A10 A11 2−7.9323217E+00  1.3167649E+01 −2.5466405E+01  4.4798603E+01−2.3135765E+01 3 2.1775767E+02 −6.0797014E+02  9.6842286E+02−5.9880217E+02  −6.6124841E+02 4 −1.9342767E+01  6.5929115E+01−6.4529964E+01  −6.1266860E+01   1.2963567E+02 5 2.9522632E−011.6440532E+01 −4.1345649E+01  3.7918438E+01 −6.4575122E+00 6−5.0018582E+01  1.4658593E+02 −1.9373147E+02  6.6223449E+01 2.1711729E+01 7 8.8248022E+00 −8.7679024E+00  −1.7315292E+01 7.8492511E+01 −1.4622206E+02 8 2.8820455E+02 −6.3379339E+02 8.3228049E+02 −5.3848211E+02  −9.4960300E+01 9 4.7051699E+00−1.7168568E+01  2.8910623E+01 −2.3853611E+01   4.2860504E+00 109.3260807E−02 −5.5053436E−01  3.5015027E−01 4.5157945E−02 −1.3115015E−0111 1.4056369E−01 −5.5181593E−01  5.8217227E−01 −2.5346130E−01  2.2533443E−02 A12 A13 A14 A15 A16 2 −4.1168856E+01  3.6126687E+014.5167107E+01 −6.6909343E+01   2.2906379E+01 3 1.5953742E+03−1.1639155E+03  1.8095955E+02 1.8323577E+02 −7.2162690E+01 46.5777501E+01 −2.5888581E+02  1.6157272E+02 −1.1278136E+00 −1.8606587E+01 5 8.4136618E+00 −4.7121013E+01  5.4842045E+01−2.5712614E+01   4.4022586E+00 6 2.4042348E+02 −5.3939285E+02 4.0698032E+02 −9.7387580E+01  −8.5024431E+00 7 1.4984421E+02−5.9580203E+01  −3.3782352E+01  4.4029934E+01 −1.2959937E+01 84.9714801E+02 −4.4021903E+02  2.0561553E+02 −5.5140373E+01  7.1800820E+00 9 7.2388190E+00 −3.2801218E+00  −2.1588996E+00 1.9395197E+00 −4.0497145E−01 10 7.3887197E−02 −3.4671609E−02 1.3344559E−02 −2.8389257E−03   2.2595546E−04 11 1.2655940E−024.4837489E−03 −6.3548912E−03  1.9856344E−03 −2.1370545E−04

TABLE 9 Example 5 f = 3.789, Bf = 1.093, Fno. = 2.04, 2ω = 77.4 Si Ri DiNdj νdj 1 (aperture stop) ∞ −0.262 *2 1.41353 0.658 1.54488 54.87 *3−10.79696 0.092 *4 −2.44956 0.263 1.63350 23.62 *5 56.69982 0.249 *65.10382 0.264 1.63350 23.62 *7 8.42791 0.367 *8 −1.96203 0.525 1.5448854.87 *9 −1.14051 0.458 *10  7.73493 0.354 1.54488 54.87 *11  1.403500.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.547 14 (imaging surface) ∞*aspherical surface

TABLE 10 Example 5: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2  1.6350612E−01 0.0000000E+00 −1.5566968E−01 −5.4479688E−011.2204184E+01 3 −6.8991586E+00 0.0000000E+00 −1.7195914E−02 1.4166815E+00 −1.2623386E+01  4 −2.9718839E+00 0.0000000E+00 5.2636053E−01 −3.2364423E−01 3.1910603E+00 5 −1.0000009E+010.0000000E+00  3.1821423E−01  1.9394976E−01 −2.4577170E+00  6−3.4432593E−01 0.0000000E+00  1.4354066E−01 −7.1394042E−01 1.2645805E−017 −6.2066909E+00 0.0000000E+00  1.0713384E−01 −2.8715051E−01−9.4973563E−01  8  8.8356189E−01 0.0000000E+00 −1.3113958E−01−3.8225567E−01 7.5306156E+00 9 −2.5263117E−01 0.0000000E+00 3.2259942E−01 −2.3108093E+00 9.2093818E+00 10  8.4921599E+000.0000000E+00 −3.8567860E−01  5.6565807E−02 4.2088260E−01 11−2.0297980E−01 0.0000000E+00 −8.3808710E−01  1.9777765E+00−5.1759204E+00  A7 A8 A9 A10 A11 2 −5.2414055E+01 9.5504435E+01−5.3867309E+01 −2.9048099E+01 −1.0915593E+02  3  6.5028371E+01−1.8210089E+02   2.3973878E+02 −5.4173530E+01 −1.1803718E+01  4−3.2720125E+01 1.0577862E+02 −1.3000851E+02 −1.6310754E+01 1.6271680E+025  6.8918886E+00 −7.1195733E+00  −7.7717931E+00  2.4337175E+01−1.1976929E+01  6 −6.7828458E+00 4.2774204E+01 −8.3703616E+01 4.5021526E+01 2.1640985E+01 7  1.5020412E+00 4.2800807E+00−1.0517606E+01  6.7258096E+00 −1.5565720E+01  8 −2.8847792E+013.8828662E+01  4.3033368E+01 −2.3464563E+02 3.4789319E+02 9−2.2016773E+01 3.0140955E+01 −1.7064024E+01 −8.8639504E+00 1.6993878E+0110 −1.7249926E−01 −1.4648670E−01  −2.1284628E−02  1.0720170E−015.6584158E−03 11  1.1383054E+01 −1.7419787E+01   1.8876101E+01−1.5129497E+01 9.1717063E+00 A12 A13 A14 A15 A16 2  4.7727873E+02−6.2712730E+02   3.8091682E+02 −9.8632806E+01 5.0298914E+00 3−8.2205140E+02 2.1459208E+03 −2.3628738E+03  1.2645200E+03−2.7101601E+02  4 −5.0846767E+01 −1.0321592E+02   2.5138387E+01 7.2998915E+01 −3.6760188E+01  5 −9.4145239E+00 7.3409114E−02 1.6590317E+01 −1.1458086E+01 1.9943686E+00 6  2.6933120E+01−6.0502441E+01  −6.5549028E+01  1.3589402E+02 −5.5641609E+01  7 4.8158682E+01 −5.4224902E+01   1.8999999E+01  5.3779358E+00−3.7050255E+00  8 −1.8910847E+02 −9.6603393E+01   2.0356861E+02−1.1426899E+02 2.3135240E+01 9 −3.1258182E+00 −8.0420300E+00  6.6478805E+00 −2.1015355E+00 2.4705859E−01 10 −3.0714008E−02−1.7346354E−03   7.0669032E−03 −1.6976411E−03 8.3775698E−05 11−4.1754698E+00 1.3781310E+00 −3.0895580E−01  4.1793744E−02−2.5625462E−03 

TABLE 11 Example 6 f = 3.669, Bf = 1.199, Fno. = 2.02, 2ω = 78.6 Si RiDi Ndj νdj 1 (aperture stop) ∞ −0.262 *2 1.41852 0.629 1.54488 54.87 *3−11.99658 0.094 *4 −2.35826 0.263 1.63350 23.62 *5 64.69279 0.236 *64.63090 0.263 1.63350 23.62 *7 6.70602 0.354 *8 −1.98230 0.511 1.5448854.87 *9 −1.02969 0.445 *10  62.29807 0.327 1.54488 54.87 *11  1.671830.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.652 14 (imaging surface) ∞*aspherical surface

TABLE 12 Example 6: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2 1.7173966E−01 0.0000000E+00  5.7870823E−02 −5.1432576E−01  4.1766914E+00 3 −5.3119375E+00  0.0000000E+00 −9.8395844E−012.2886213E+01 −2.0548991E+02 4 −6.8683709E+00  0.0000000E+00 4.3190249E−01 9.2344049E−01 −6.0508176E+00 5 1.0000040E+010.0000000E+00  2.5714641E−01 9.7620423E−01 −2.7058081E+00 6−7.5252455E+00  0.0000000E+00 −4.3424298E−01 1.6093247E+00 8.4538117E−02 7 7.2365736E+00 0.0000000E+00 −7.3440018E−02−1.3837986E−01   7.8051515E−01 8 1.4256110E+00 0.0000000E+00−6.7544765E−01 8.8039828E+00 −5.5306195E+01 9 −6.2344100E−01 0.0000000E+00 −1.7449228E+00 2.5167366E+01 −1.4781348E+02 104.1837471E+00 0.0000000E+00 −3.5010091E−01 1.6410410E−01  2.1277866E−0111 −8.6899387E−02  0.0000000E+00 −5.7091068E−01 4.2283769E−01 3.0543423E−01 A7 A8 A9 A10 A11 2 −1.7676854E+01  4.3203858E+01−5.6956704E+01 2.3518390E+01  2.9662604E+01 3 1.0311229E+03−3.1791483E+03   6.1780944E+03 −7.3166228E+03   4.4409571E+03 48.4738407E+00 2.4916266E+00 −3.7456312E+00 −2.0654796E+01 −3.5921371E+01 5 2.2404916E−01 4.8469708E+00 −4.9312124E−01−1.2710114E+01   2.0139576E+01 6 −1.9394803E+01  5.7145701E+01−6.7448564E+01 3.4166444E+01 −6.4648671E+01 7 −1.2905721E+00 −1.8573573E+00   1.0375531E+01 −1.7621424E+01   9.8878709E+00 82.0078906E+02 −4.5221396E+02   6.5422639E+02 −6.2665551E+02  4.4475402E+02 9 4.5457998E+02 −7.5196362E+02   4.5197858E+027.0319605E+02 −1.9014229E+03 10 3.9318078E−02 −4.1717742E−01  2.0464243E−01 1.0386404E−01 −1.0561531E−01 11 −6.7934374E−01 4.5028268E−01 −1.5558371E−01 5.3770525E−02 −3.4646885E−02 A12 A13 A14A15 A16 2 −2.6392450E+01  −2.1532391E+01   3.5024591E+01 −1.3534804E+01  9.6888965E−01 3 −4.2578513E+01  −1.5823922E+03   5.4831363E+022.3741806E+02 −1.3160053E+02 4 2.0207658E+02 −2.1325994E+02  9.4745660E−03 1.1215071E+02 −4.6772823E+01 5 −1.3679193E+01 −1.2278118E+01   4.1489417E+01 −3.7120245E+01   1.1266315E+01 61.5330358E+02 −4.2249375E+01  −2.3728407E+02 2.8280421E+02−9.8054975E+01 7 9.4831264E+00 −1.3346011E+01  −2.6787286E+001.0387073E+01 −4.0429551E+00 8 −3.1412997E+02  2.4040160E+02−1.3827952E+02 4.3740850E+01 −5.4229599E+00 9 2.0848336E+03−1.3195386E+03   4.9588146E+02 −1.0176029E+02   8.6102881E+00 102.3762965E−02 7.5713421E−04 −1.2886464E−03 5.3309100E−04 −1.0452550E−0411 1.7083384E−02 −4.0009703E−03  −2.4409284E−05 2.2353696E−04−3.5715816E−05

TABLE 13 Example 7 f = 3.826, Bf =1.028, Fno. = 2.01, 2ω = 76.6 Si Ri DiNdj νdj 1 (aperture stop) ∞ −0.262E *2 1.40767 0.641 1.54488 54.87 *3−9.83659 0.112 *4 −2.42423 0.275 1.63350 23.62 *5 69.74598 0.255 *64.71474 0.281 1.63350 23.62 *7 6.49833 0.380 *8 −1.90504 0.524 1.5448854.87 *9 −1.06918 0.471 *10  −11.99865 0.354 1.54488 54.87 *11  1.832770.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.482 14 (imaging surface) ∞*aspherical surface

TABLE 14 Example 7: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2 −2.5387995E−01 0.0000000E+00 −1.2108971E−01 −1.6320763E−01  6.7872343E+00 3 −1.0000009E+01 0.0000000E+00 −1.2616134E+002.4311833E+01 −1.9173218E+02 4 −1.1309304E−01 0.0000000E+00 4.8849889E−01 9.7344465E−01 −5.4123915E+00 5 −1.0000009E+010.0000000E+00  3.7199068E−01 2.9893156E−01 −2.5096218E+00 6−5.7503340E+00 0.0000000E+00  1.6606073E−01 −1.1109723E+00  4.3310918E+00 7  1.0000009E+01 0.0000000E+00  8.1808756E−032.1928292E−02 −5.3214958E−01 8  1.6181914E+00 0.0000000E+00 5.4894637E−02 −3.6315520E+00   3.3711090E+01 9 −1.0116597E+000.0000000E+00  1.6410926E−01 −2.1382469E+00   9.7819479E+00 10−1.0000015E+01 0.0000000E+00 −4.1351382E−01 2.0685786E−01  2.8515367E−0111 −2.6583118E−01 0.0000000E+00 −6.2636623E−01 4.5803563E−01 3.2740894E−01 A7 A8 A9 A10 A11 2 −2.8032242E+01 4.8976817E+01−2.5206855E+01 −4.6081241E+01   8.9458274E+01 3  8.3411397E+02−2.1005850E+03   2.8499484E+03 −1.1643528E+03  −1.9399095E+03 4 2.6697445E+00 1.8226113E+01 −1.8603726E+01 −4.2038277E+01  6.3700173E+01 5  4.3888843E+00 2.7997711E+00 −2.9781939E+014.8042566E+01  4.2698928E+00 6 −2.5189389E+01 8.4868527E+01−1.2001491E+02 −1.5635857E+01   2.0975378E+02 7 −4.6553334E−015.6673603E+00 −1.0949152E+01 7.9826853E+00 −6.4384686E+00 8−1.4369376E+02 3.4831770E+02 −4.8798434E+02 3.2400874E+02  5.9915975E+019 −2.6166887E+01 4.5741990E+01 −5.6922321E+01 5.7519198E+01−5.3477012E+01 10 −6.2975650E−02 −3.6133859E−01   2.1212622E−015.3531033E−02 −4.7994342E−02 11 −6.7622051E−01 3.9008070E−01−7.9616843E−02 −1.0325713E−03  −8.3168406E−03 A12 A13 A14 A15 A16 2−5.9174619E+01 5.6737468E+00  1.6476693E+01 −1.1303460E+01  2.7292099E+00 3  2.1428917E+03 1.2427912E+03 −3.4082210E+032.2154681E+03 −5.0346587E+02 4  3.0279918E+01 −6.5012405E+01 −3.8418526E+01 8.4965026E+01 −3.1604017E+01 5 −9.6972205E+011.2177533E+02 −7.5109246E+01 3.0019274E+01 −7.3907198E+00 6−1.1271735E+02 −1.4300352E+02   1.2178101E+02 3.6465963E+01−4.0072090E+01 7  1.2065571E+01 1.3818045E+00 −2.9587431E+013.0152934E+01 −9.4105584E+00 8 −2.4266492E+02 8.7560180E+01 8.3718692E+01 −7.7836362E+01   1.8565257E+01 9  4.4329416E+01−2.8044601E+01   1.1737890E+01 −2.8304059E+00   2.9692006E−01 10−1.1869924E−02 1.0372074E−02 −2.3138292E−04 −6.4392027E−04  8.0226256E−05 11  9.7299034E−03 −3.7663742E−03   5.7787457E−043.2625287E−05 −1.6221991E−05

TABLE 15 Example 8 f = 3.742, Bf =1.187, Fno. = 2.05, 2ω = 78.0 Si Ri DiNdj νdj 1 (aperture stop) ∞ −0.262 *2 1.42075 0.635 1.54488 54.87 *3−12.41332 0.099 *4 −2.39412 0.263 1.63350 23.62 *5 69.33297 0.236 *64.65396 0.264 1.63350 23.62 *7 6.65762 0.354 *8 −2.01009 0.511 1.5448854.87 *9 −1.02280 0.445 *10  −26.20072 0.327 1.54488 54.87 *11  1.719380.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.641 14 (imaging surface) ∞*aspherical surface

TABLE 16 Example 8: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2  1.1993594E−01 0.0000000E+00 7.6263416E−02 1.2094509E+00−1.6347140E+01 3 −3.6555446E+00 0.0000000E+00 −3.6217322E−01 1.3834455E+01 −1.9017460E+02 4 −5.0488052E+00 0.0000000E+002.0343823E−01 1.5164165E+00 −2.7231259E+00 5  1.0000009E+010.0000000E+00 1.6240499E−01 1.1624678E+00 −2.7776204E+00 6−6.3864636E+00 0.0000000E+00 −3.4245539E−01  1.8291615E+00−6.1351381E+00 7  1.0000009E+01 0.0000000E+00 2.3755410E−02−4.0948243E−01  −4.5645039E−01 8  1.4639713E+00 0.0000000E+00−9.4082941E−02  −7.4305415E−01   1.4039826E+01 9 −6.6969478E−010.0000000E+00 2.6762681E−01 −1.8979566E+00   7.1152661E+00 10−7.8266990E+00 0.0000000E+00 −3.4935867E−01  1.4374094E−01 3.9540410E−01 11  7.9614263E−02 0.0000000E+00 −5.9651557E−01 4.5832144E−01  2.0912982E−01 A7 A8 A9 A10 A11 2  7.4088634E+01−1.4809496E+02  7.7207762E+01 1.9298188E+02 −3.0105786E+02 3 1.3973043E+03 −6.1638304E+03  1.7476541E+04 −3.2956821E+04  4.1559976E+04 4 −9.5745201E+00 3.1184209E+01 −1.2413989E+01 −5.1985105E+01   6.5374186E+01 5 −1.0350687E−01 4.9795980E+002.2441804E+00 −1.4090479E+01   5.7520686E+00 6  1.6105829E+01−5.6127342E+01  1.5063962E+02 −1.9560685E+02  −7.2595928E+00 7 4.9617266E+00 −9.5759012E+00  4.1449188E+00 4.3561551E+00 2.7096732E+00 8 −7.8811508E+01 2.3549884E+02 −4.0824950E+02 3.8290924E+02 −9.7413669E+01 9 −1.6491270E+01 2.2176629E+01−1.3593636E+01  −1.5236261E+00   4.8210280E+00 10 −3.6751312E−016.7366712E−03 3.8210552E−02 −8.0794000E−03   8.1019027E−02 11−4.5067483E−01 1.3689620E−01 1.0223419E−01 −7.4988960E−02 −6.2729741E−04 A12 A13 A14 A15 A16 2 −2.6596222E+01 3.7059343E+02−3.1037887E+02  8.9826583E+01 −3.5043586E+00 3 −3.4075628E+041.6567180E+04 −3.3936201E+03  −5.1806665E+02   2.8364429E+02 4−1.2566531E+01 −2.2241519E+00  −2.1739023E+01  1.8705158E+01−3.5890969E+00 5  4.4527221E+00 1.7397532E+00 5.3372360E+00−1.6979772E+01   8.3184671E+00 6  3.3631252E+02 −3.4922615E+02 3.7787087E+01 1.3138073E+02 −5.9757425E+01 7 −2.1092691E+013.6090355E+01 −4.0454083E+01  2.7129762E+01 −7.5675472E+00 8−1.6274391E+02 1.5396797E+02 −2.1143393E+01  −2.6698987E+01  9.5152966E+00 9  1.8846698E+00 −4.1837709E+00  1.3709078E+002.0197760E−01 −1.2169776E−01 10 −7.6421242E−02 1.5931851E−026.6628782E−03 −3.3398307E−03   3.9740851E−04 11  1.6507326E−02−6.3078063E−03  4.4012870E−04 2.5172166E−04 −4.7922106E−05

TABLE 17 Example 9 f = 3.769, Bf = 1.083, Fno. = 2.01, 2ω = 78.0 Si RiDi Ndj νdj 1 (aperture stop) ∞ −0.262 *2 1.37836 0.639 1.54488 54.87 *326.20119 0.116 *4 −2.48307 0.263 1.63350 23.62 *5 −12.30867 0.249 *65.20297 0.263 1.63350 23.62 *7 8.41742 0.367 *8 −1.98256 0.527 1.5448854.87 *9 −1.13769 0.463 *10  7.81265 0.354 1.54488 54.87 *11  1.382890.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.537 14 (imaging surface) ∞*aspherical surface

TABLE 18 Example 9: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2 1.5188996E−01 0.0000000E+00 −1.6427892E−01  −1.9518618E−01 9.2551567E+00 3 9.1745677E+00 0.0000000E+00 −1.2777419E−01  1.9518374E+00 −1.9169265E+01 4 −3.2767628E+00  0.0000000E+003.7156277E−01  1.5497536E+00 −1.5409411E+01 5 8.9352602E+000.0000000E+00 1.0458738E−01  1.0328843E+00 −2.2034262E+00 63.2294049E+00 0.0000000E+00 −1.5856249E−01   7.3831558E−01−4.3346938E+00 7 −1.0000010E+01  0.0000000E+00 1.0979453E−02−3.0160430E−01  8.7119630E−01 8 1.3383869E+00 0.0000000E+00−3.8625674E−01   2.2507690E+00 −5.8526525E+00 9 −2.2773386E−01 0.0000000E+00 5.0564717E−01 −4.1327985E+00  1.7093726E+01 106.5923540E+00 0.0000000E+00 −4.4646980E−01   1.5079196E−02 6.5847200E−01 11 −3.7900479E−01  0.0000000E+00 −7.2475815E−01  6.8405182E−01 −2.6801750E−01 A7 A8 A9 A10 A11 2 −4.1573852E+01 8.8536864E+01 −1.0931517E+02   1.0100776E+02 −1.1048279E+02 31.2123068E+02 −4.5743974E+02  1.0315302E+03 −1.3095543E+03 6.0833239E+02 4 5.6456231E+01 −1.1600759E+02  1.4209150E+02−7.9385193E+01 −6.2960025E+01 5 1.5449192E+00 −4.0887923E+00 1.3191385E+01 −1.5601606E+01  1.6250985E+01 6 1.1982610E+01−1.9756832E+01  1.8409505E+01  1.0940030E+01 −8.6112591E+01 7−4.9466423E+00  1.6300286E+01 −2.6499697E+01   1.6019777E+01 1.1653440E+01 8 5.5155570E+00 1.6708764E+01 −7.0279667E+01  1.0808552E+02 −6.6688316E+01 9 −3.8275303E+01  3.5504923E+013.3618893E+01 −1.3574116E+02  1.6853397E+02 10 −4.4301180E−01 4.8250846E−02 −6.8176479E−02  −1.0071284E−02  1.1900655E−01 115.0811740E−01 −9.6452859E−01  7.6546097E−01 −2.1151064E−01−6.9082624E−02 A12 A13 A14 A15 A16 2 1.2786210E+02 −1.0135902E+02 4.8273426E+01 −1.4365520E+01  2.5499221E+00 3 6.6215757E+02−1.1820261E+03  6.7497116E+02 −1.1755737E+02 −1.4336131E+01 41.3621444E+02 3.0025047E+01 −2.6698695E+02   2.4993994E+02−7.5755921E+01 5 −3.1317011E+01  2.3367125E+01 2.0225462E+01−3.4480070E+01  1.2187977E+01 6 1.2351493E+02 2.0048743E+01−2.2605554E+02   2.2074129E+02 −7.0329364E+01 7 −3.2822400E+01 4.1952075E+01 −3.9909107E+01   2.3378985E+01 −5.8226623E+00 8−5.8015365E+00  7.2521054E+00 3.3149774E+01 −3.2892367E+01 8.9410881E+00 9 −1.0526388E+02  2.7758688E+01 3.8129682E+00−4.1031262E+00  7.2222814E−01 10 −2.4510163E−02  −6.0418210E−02 4.2078600E−02 −1.0620013E−02  9.6649492E−04 11 5.7447664E−02−2.6227852E−03  −8.2366497E−03   2.9171736E−03 −3.2296344E−04

TABLE 19 Example 10 f = 3.787, Bf = 1.055, Fno. = 2.04, 2ω = 78.6 Si RiDi Ndj νdj 1 (aperture stop) ∞ −0.262 *2 1.37237 0.629 1.54488 54.87 *340.94323 0.107 *4 −2.42531 0.263 1.63350 23.62 *5 −14.34654 0.262 *64.70449 0.263 1.63350 23.62 *7 7.26101 0.379 *8 −1.93091 0.524 1.5448854.87 *9 −1.05748 0.487 *10  −17.10748 0.354 1.54488 54.87 *11  1.664150.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.508 14 (imaging surface) ∞*aspherical surface

TABLE 20 Example 10: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2  1.5224648E−01 0.0000000E+00 −5.3698504E−02 −1.8831936E+00  2.0043831E+01 3 −1.0000025E+01 0.0000000E+00  1.6825073E−01−2.9174159E+00   1.2386011E+01 4 −6.2639159E+00 0.0000000E+00 3.4617175E−01 −5.0156650E−01   3.4610293E+00 5 −7.7517405E+000.0000000E+00 −3.4527076E−02 1.1228866E+00 −2.7676352E+00 6−9.1874099E+00 0.0000000E+00 −1.7600375E−01 6.3734471E−01 −1.0678397E+007  6.4045096E+00 0.0000000E+00 −1.6377765E−02 6.4421351E−02−1.5731771E+00 8  1.5373747E+00 0.0000000E+00 −2.3553117E−01−9.8410720E−02   1.4293475E+01 9 −9.6625265E−01 0.0000000E+00 2.6395741E−01 −1.5064896E+00   4.2442333E+00 10 −1.0000021E+010.0000000E+00 −3.6451914E−01 1.9334961E−01  1.8433518E−01 11−4.7000612E−01 0.0000000E+00 −6.2625510E−01 4.7172735E−01  3.0255541E−01A7 A8 A9 A10 A11 2 −8.2375712E+01 1.7513885E+02 −1.7046817E+02−3.7339803E+01   2.5511754E+02 3  7.4695951E−01 −1.2439597E+02  2.8518340E+02 −7.3514887E+01  −4.4104034E+02 4 −2.9001799E+011.0344992E+02 −1.7365371E+02 1.2135184E+02 −5.1109079E+00 5 9.8206775E+00 −3.4533537E+01   6.0399794E+01 −3.5782087E+01 −1.9530289E+01 6 −1.0318248E+01 4.9393561E+01 −9.5355412E+011.0523194E+02 −9.5889367E+01 7  5.0679248E+00 −1.1794908E+01  2.1452518E+01 −2.1651807E+01   1.2003984E+00 8 −9.0410031E+012.9363395E+02 −5.6556495E+02 6.2919506E+02 −3.0491989E+02 9−7.9335273E+00 9.6139187E+00 −6.2026167E+00 1.9554636E+00 −2.9126700E+0010  5.5319481E−02 −3.0073691E−01  −1.6103232E−01 5.9483677E−01−4.7573648E−01 11 −6.5541797E−01 4.0679948E−01 −1.2636570E−012.4442983E−02  6.8171257E−03 A12 A13 A14 A15 A16 2 −1.7506591E+02−9.8664022E+01   2.0411615E+02 −1.0848395E+02   1.9933129E+01 3 1.3687051E+02 1.2338127E+03 −1.9540460E+03 1.2035392E+03 −2.7684575E+024  1.3651562E+01 −7.9638254E+01   3.7638765E+01 2.3573249E+01−1.5438200E+01 5  3.2467596E+01 −4.0576659E+01   8.2018395E+01−7.6641371E+01   2.4220415E+01 6  4.3854140E+01 1.6570896E+02−3.9009284E+02 3.2616441E+02 −9.8486498E+01 7  1.1511462E+011.1899116E+01 −3.5946229E+01 2.6147642E+01 −6.4856933E+00 8−1.1357924E+02 2.2564836E+02 −9.4773399E+01 1.2316178E+00  5.6112986E+009  4.4319463E+00 −1.4176260E+00  −1.4819919E+00 1.1920800E+00−2.4355517E−01 10  1.8309663E−01 −2.9725909E−02  −4.6936433E−033.2398074E−03 −4.7129506E−04 11 −2.0687375E−02 1.7142438E−02−7.3290023E−03 1.6545930E−03 −1.5657508E−04

TABLE 21 Example 11 f = 3.767, Bf = 1.082, Fno. = 2.03, 2ω = 77.8 Si RiDi Ndj νdj 1 (aperture stop) ∞ −0.262 *2 1.36643 0.635 1.54488 54.87 *343.66000 0.092 *4 −3.14515 0.263 1.63350 23.62 *5 43.91061 0.249 *64.96666 0.288 1.63350 23.62 *7 8.18620 0.367 *8 −1.86301 0.529 1.5448854.87 *9 −1.15019 0.458 *10  7.28772 0.360 1.54488 54.87 *11  1.484750.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.535 14 (imaging surface) ∞*aspherical surface

TABLE 22 Example 11: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2 1.7070520E−01 0.0000000E+00 −1.4199015E−01  9.9423248E−01−2.9012865E+00 3 4.5243395E+00 0.0000000E+00 −7.9996585E−01 1.5898231E+01 −1.2969356E+02 4 −4.2569412E+00  0.0000000E+002.4238286E−01 5.1544244E−01 −2.8983841E+00 5 1.0000183E+01 0.0000000E+001.1298094E−01 8.5316246E−01 −2.8519256E+00 6 8.9449996E+00 0.0000000E+00−1.2232526E−01  3.4529635E−01 −1.2565484E+00 7 8.7012842E+000.0000000E+00 1.0028839E−01 −4.7221366E−01  −8.3788810E−01 86.9624559E−01 0.0000000E+00 −4.0286705E−01  5.7723215E+00 −3.2928760E+019 −2.8709793E−01  0.0000000E+00 2.3945755E−01 −1.2594768E+00  3.9904439E+00 10 8.3956604E+00 0.0000000E+00 −2.8807613E−01 1.5408703E−01 −1.3195829E−01 11 1.6175499E−01 0.0000000E+00−5.2826117E−01  3.7883825E−01  1.6127654E−01 A7 A8 A9 A10 A11 21.0914357E+01 −4.2455525E+01  9.9393349E+01 −1.0912240E+02 −4.9239027E+00 3 5.8096944E+02 −1.4995077E+03  2.0528634E+03−6.6652093E+02  −2.1292565E+03 4 4.3126438E+00 −4.7765606E+00 2.5859546E+01 −7.6950299E+01   8.2840177E+01 5 3.7476907E+00−3.0509825E+00  5.5782053E+00 −9.9070953E+00   1.3366021E+00 6−4.6652262E−01  2.8202009E+00 2.5897781E+01 −1.1536623E+02  1.8151862E+02 7 7.1614707E+00 −1.5259984E+01  1.0864650E+015.1480077E+00 −1.1230610E+01 8 1.0370450E+02 −1.8547548E+02 1.6274798E+02 5.5230620E+00 −1.5045958E+02 9 −7.6586255E+00 8.1905580E+00 −1.6489500E+00  −7.3716775E+00   8.6329509E+00 104.6437454E−01 −5.9579287E−01  1.8307057E−01 1.9184636E−01 −1.2887296E−0111 −4.4407479E−01  2.6587597E−01 1.0636022E−04 −7.6291561E−02  3.2142495E−02 A12 A13 A14 A15 A16 2 1.5042827E+02 −1.6036920E+02 6.1730441E+01 1.5110475E+00 −5.0076040E+00 3 2.8451465E+03−2.7887501E+02  −1.9723278E+03  1.5752735E+03 −3.9319500E+02 4−8.2185567E−02  −3.8987967E+01  −2.9688448E+01  6.4229151E+01−2.4502191E+01 5 1.4771896E+01 9.2018156E−01 −4.2900106E+01 4.8473671E+01 −1.6906580E+01 6 −1.2754393E+02  8.3859688E+01−1.5807075E+02  1.6937206E+02 −6.1389335E+01 7 6.3433638E+00−6.6537125E+00  7.7634820E+00 −3.1403309E+00   1.1529994E−01 81.2295234E+02 −2.1335247E+01  −1.6212538E+01  6.0877177E+00 6.3569772E−02 9 −2.4964147E+00  −1.2369939E+00  5.3790357E−012.3616181E−01 −1.0658729E−01 10 −5.4990833E−02  9.2705449E−02−4.5279400E−02  1.0662748E−02 −1.0325438E−03 11 −1.2376816E−03 1.4377558E−04 −1.9563885E−03  8.7469519E−04 −1.1444433E−04

TABLE 23 Example 12 f = 3.810, Bf =1.047, Fno. = 2.01, 2ω = 76.4 Si RiDi Ndj νdj 1 (aperture stop) ω −0.262 *2 1.36442 0.639 1.54488 54.87 *342.90783 0.125 *4 −2.70075 0.275 1.63350 23.62 *5 81.85147 0.249 *64.30365 0.280 1.63350 23.62 *7 7.53886 0.369 *8 −1.96839 0.525 1.5448854.87 *9 −1.07644 0.485 *10  −11.93508 0.354 1.54488 54.87 *11  1.848160.408 12 ∞ 0.210 1.51633 64.14 13 ∞ 0.501 14 (imaging surface) ∞*aspherical surface

TABLE 24 Example 12: Aspherical Surface Data Surface Number KA A3 A4 A5A6 2 −2.3069285E−01 0.0000000E+00 −2.3806040E−01  1.2419921E+00−3.3688527E+00 3 −1.0000008E+01 0.0000000E+00 −7.9573008E−01 1.3885198E+01 −1.2702593E+02 4 −5.7861729E−02 0.0000000E+00 3.4641512E−01  3.3192039E−01 −4.5781706E+00 5  1.0000009E+010.0000000E+00 −9.2477651E−02  8.9189913E−01 −2.1744271E−01 6 3.2671936E+00 0.0000000E+00 −7.6199665E−02 −3.9244545E−01−1.3311370E+00 7  9.2122756E+00 0.0000000E+00  3.7349240E−02−3.3368966E−01 −7.2065218E−01 8  1.7545340E+00 0.0000000E+00 2.4935506E−01 −8.3484070E+00  7.1388222E+01 9 −9.8034463E−010.0000000E+00  2.3614818E−01 −2.6674020E+00  1.1691275E+01 10−1.0000032E+01 0.0000000E+00 −3.6491284E−01  1.9441855E−01 1.8692083E−01 11  1.2544876E−01 0.0000000E+00 −5.8379722E−01 4.8697271E−01  2.1799281E−02 A7 A8 A9 A10 A11 2  2.0298762E+01−9.4692380E+01   2.3426779E+02 −3.0289600E+02  1.4692552E+02 3 6.9101126E+02 −2.3425331E+03   5.0709516E+03 −6.9556827E+03 5.6389040E+03 4  8.3851163E+00 1.5917600E+00  2.8146048E+00−7.8284118E+01  1.4232581E+02 5 −9.2660514E−01 −2.3303626E+00 −1.0367032E+01  5.1780994E+01 −3.2140369E+01 6  9.0097115E+00−1.7030212E+01   1.5795429E+01 −2.8702286E+01  6.0637353E+01 7 2.6548511E+00 −1.7779146E+00   4.6976965E+00 −2.8090336E+01 5.4714461E+01 8 −3.0968218E+02 7.9993295E+02 −1.2692832E+03 1.1501132E+03 −3.5967408E+02 9 −2.9212740E+01 4.2221350E+01−2.9657864E+01 −2.9055932E+00  2.2496993E+01 10 −6.1775797E−02−1.2692401E−01  −2.0209953E−01  5.1207881E−01 −3.6786237E−01 11−1.3459927E−01 −1.4897639E−01   2.7472673E−01 −1.9214064E−01 1.2998945E−01 A12 A13 A14 A15 A16 2  1.2740212E+02 −2.6016230E+02  1.9479308E+02 −7.7310333E+01  1.3786763E+01 3 −1.9802876E+03−5.6339009E+02   7.4558845E+02 −1.8912672E+02 −1.5421209E+00 4−6.8779874E+01 −7.6362937E+00  −4.7643561E+01  8.3010445E+01−3.1743271E+01 5 −7.6691349E+01 9.0154866E+01  2.6482694E+01−7.0946330E+01  2.4582863E+01 6 −6.0335334E+01 7.7436809E+01−1.7083244E+02  1.8258159E+02 −6.7209507E+01 7 −5.5326973E+015.4419420E+01 −6.4136411E+01  4.7249923E+01 −1.3530469E+01 8−3.5438251E+02 4.1475469E+02 −1.3609676E+02 −9.0025917E+00 1.0055197E+01 9 −1.6229965E+01 3.3501082E+00  1.3607840E+00−8.1711446E−01  1.2022703E−01 10  9.9417768E−02 1.3382468E−02−1.7581966E−02  5.1468751E−03 −5.7080172E−04 11 −1.0815188E−016.8453592E−02 −2.6152539E−02  5.4265135E−03 −4.7393917E−04

TABLE 25 Values Related to Conditional Formulae Formula ConditionExample 1 Example 2 Example 3 Example 4 Example 5 Example 6 1 f/f1 1.571.38 1.58 1.54 1.62 1.56 2 f/f4 0.93 1.40 1.06 1.12 0.93 1.12 3 f/f5−1.19 −1.59 −1.36 −1.27 −1.18 −1.17 4 TTL/(f · tanω) 1.46 1.42 1.42 1.421.42 1.43 5 L1f/Φ 0.76 0.82 0.76 0.78 0.76 0.77 6 f · tanω/L5 r 2.142.46 1.81 1.76 2.16 1.81 Formula Condition Example 7 Example 8 Example 9Example 10 Example 11 Example 12 1 f/f1 1.66 1.57 1.42 1.46 1.46 1.48 2f/f4 1.04 1.16 0.94 1.07 0.86 1.06 3 f/f5 −1.32 −1.27 −1.20 −1.37 −1.08−1.31 4 TTL/(f · tanω) 1.43 1.43 1.42 1.39 1.42 1.45 5 L1f/Φ 0.74 0.780.74 0.74 0.74 0.72 6 f · tanω/L5 r 1.65 1.76 2.21 1.86 2.05 1.62

Note that the above paraxial radii of curvature, the distances amongsurfaces, the refractive indices, and the Abbe's numbers were obtainedby measurements performed by specialists in the field of opticalmeasurement, according to the methods described below.

The paraxial radii of curvature were obtained by measuring the lensesusing an ultra high precision three dimensional measurement device UA3P(by Panasonic Factory Solutions K. K) by the following procedures. Aparaxial radius of curvature R_(m) (m is a natural number) and a conicalcoefficient K_(m) are preliminarily set and input into UA3P, and an nthorder aspherical surface coefficient An of an aspherical shape formulais calculated from the input paraxial radius of curvature R_(m) andconical coefficient K_(m) and the measured data, using a fittingfunction of UA3P. C=1/R_(m) and KA=K_(m)−1 are considered in theaforementioned aspherical surface shape formula (A). Depths Z of anaspherical surface in the direction of the optical axis corresponding toheights h from the optical axis are calculated from R_(m), K_(m), An,and the aspherical surface shape formula. The difference between thecalculated depths Z and actually measured depth values Z′ are obtainedfor each height h from the optical axis. Whether the difference iswithin a predetermined range is judged. In the case that the differenceis within the predetermined range, R_(m) is designated as the paraxialradius of curvature. On the other hand, in the case that the differenceis outside the predetermined range, the value of at least one of R_(m)and K_(m) is changed, set as R_(m+1) and K_(m+1), and input to UA3P. Theprocesses described above are performed, and judgment regarding whetherthe difference between the calculated depths Z and actually measureddepth values Z′ for each height h from the optical axis is within apredetermined range is judged. These procedures are repeated until thedifference between the calculated depths Z and actually measured depthvalues Z′ for each height h from the optical axis is within apredetermined range. Note that here, the predetermined range is set tobe 200 nm or less. In addition, a range from 0 to ⅕ the maximum lensouter diameter is set as the range of h.

The distances among surfaces are obtained by measurements using OptiSurf(by Trioptics), which is an apparatus for measuring the centralthicknesses and distances between surfaces of paired lenses.

The refractive indices are obtained by performing measurements in astate in which the temperature of a measurement target is 25° C., usingKPR-2000 (by K. K. Shimadzu), which is a precision refractometer. Therefractive index measured with respect to the d line (wavelength: 587.6nm) is designated as Nd. Similarly, the refractive index measured withrespect to the e line (wavelength: 546.1 nm) is designated as Ne, therefractive index measured with respect to the F line (wavelength: 486.1nm) is designated as NF, the refractive index measured with respect tothe C line (wavelength: 656.3 nm) is designated as NC, and therefractive index measured with respect to the g line (wavelength: 435.8nm) is designated as Ng. The Abbe's number νd with respect to the d lineis obtained by calculations, substituting the values of Nd, NF, and NCobtained by the above measurements into the formula below.

νd=(Nd−1)/(NF−NC)

What is claimed is:
 1. An imaging lens substantially consisting of fivelenses, including: a first lens having a positive refractive power and aconvex surface toward the object side; a second lens having a negativerefractive power and a concave surface toward the object side; a thirdlens having a positive refractive power and is of a meniscus shape witha convex surface toward the object side; a fourth lens having a positiverefractive power and is of a meniscus shape with a concave surfacetoward the object side; and a fifth lens having a negative refractivepower and a concave surface toward the image side, the surface thereoftoward the image side being of an aspherical shape having at least oneinflection point within a range from an intersection of a principallight ray at a maximum angle of view with the surface toward the imageside inwardly toward the optical axis in the radial direction, providedin this order from the object side; the imaging lens satisfying thefollowing conditional formulae:1.25<f/f1<3  (1)0.57<f/f4<3  (2)−1.87<f/f5<−0.5  (3)1<TTL/(f·tan ω)<1.56  (4) wherein f is the focal length of the entiresystem, f1 is the focal length of the first lens, f4 is the focal lengthof the fourth lens, f5 is the focal length of the fifth lens, TTL is thedistance from the surface of the first lens toward the object side tothe imaging surface along the optical axis in the case that back focusis an air converted length, and ω is the half value of a maximum angleof view when focused on an object at infinity.
 2. An imaging lens asdefined in claim 1 that further satisfies the following conditionalformula:0.6<L1f/Φ<0.88  (5) wherein L1 f is the paraxial radius of curvature ofthe surface of the first lens toward the object side, and Φ is thediameter of the entrance pupil.
 3. An imaging lens as defined in claim 1that further satisfies the following conditional formula:1<f·tan ω/L5r<3  (6) wherein L5 r is the paraxial radius of curvature ofthe surface of the fifth lens toward the image side.
 4. An imaging lensas defined in claim 1, wherein: the surface of the second lens towardthe object side is of an aspherical shape having at least one inflectionpoint within a range from an intersection of a marginal axial light raywith the surface toward the object side inwardly toward the optical axisin the radial direction.
 5. An imaging lens as defined in claim 1,wherein: the surface of the third lens toward the object side is of anaspherical shape having at least one inflection point within a rangefrom an intersection of a marginal axial light ray with the surfacetoward the object side inwardly toward the optical axis in the radialdirection.
 6. An imaging lens as defined in claim 1, further comprising:an aperture stop positioned at the object side of the surface of thefirst lens toward the object side.
 7. An imaging lens as defined inclaim 1 that further satisfies the following conditional formula:1.32<f/f1<2.32  (1-1).
 8. An imaging lens as defined in claim 7 thatfurther satisfies the following conditional formula:1.32<f/f1<2  (1-2).
 9. An imaging lens as defined in claim 8 thatfurther satisfies the following conditional formula:1.35<f/f1<1.86  (1-3).
 10. An imaging lens as defined in claim 1 thatfurther satisfies the following conditional formula:0.73<f/f4<2.19  (2-1).
 11. An imaging lens as defined in claim 10 thatfurther satisfies the following conditional formula:0.8<f/f4<1.79  (2-2).
 12. An imaging lens as defined in claim 1 thatfurther satisfies the following conditional formula:−1.71<f/f5<−0.77  (3-1).
 13. An imaging lens as defined in claim 12 thatfurther satisfies the following conditional formula:−1.71<f/f5<−0.92  (3-2).
 14. An imaging lens as defined in claim 13 thatfurther satisfies the following conditional formula:−1.64<f/f5<−0.92  (3-3).
 15. An imaging lens as defined in claim 1 thatfurther satisfies the following conditional formula:1.25<TTL/(f·tan·ω)<1.49  (4-1).
 16. An imaging lens as defined in claim15 that further satisfies the following conditional formula:1.34<TTL/(f·tan·ω)<1.49  (4-2).
 17. An imaging lens as defined in claim16 that further satisfies the following conditional formula:1.34<TTL/(f·tan·ω)<1.47  (4-3).
 18. An imaging lens as defined in claim1 that further satisfies the following conditional formula:0.7<L1f/Φ<0.85  (5-1). wherein L1 f is the paraxial radius of curvatureof the surface of the first lens toward the object side, and Φ is thediameter of the entrance pupil.
 19. An imaging lens as defined in claim18 that further satisfies the following conditional formula:0.75<L1f/Φ<0.82  (5-2).
 20. An imaging apparatus comprising the imaginglens as defined in claim 1.